A Simple Conjugate Gradient Type Method for Solving Large-scale Systems of Nonlinear Equations

Abstract Quasi Newton’s method is among the most promising algorithm for solving systems of nonlinear equations. In this family, Broyden’s method update is the famous. This paper presents a simple conjugate gradient (CG) method for solving large-scale systems of nonlinear equations via memoryless Broyden’s approach. The attractive attribute of this method is due to its low memory requirements, global convergence properties and simple implementation. Under suitable conditions, the proposed method converges globally. Numerical performance of the proposed method are compared with the well-known conjugate gradients (CG) methods using benchmarks problems. The report demonstrate that the proposed method is reliable, efficient and competitive.